A192850 - OEIS

%I #16 Sep 08 2022 08:45:58

%S 46,184,414,832,1390,2232,3262,4672,6318,8440,10846,13824,17134,21112,

%T 25470,30592,36142,42552,49438,57280,65646,75064,85054,96192,107950,

%U 120952,134622,149632,165358,182520

%N Molecular topological indices of the web graphs.

%C Web graphs are defined for n>=3; extended to n=1 using closed form.

%H G. C. Greubel, <a href="/A192850/b192850.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).

%F a(n) = n*(6*n^2+22*n+3*((-1)^n+7)).

%F G.f.: 2*x*(x^4+2*x^3+46*x+23)/((x-1)^4*(x+1)^2). - _Colin Barker_, Aug 07 2012

%F E.g.f.: x*((49 +40*x +6*x^2)*exp(x) - 3*exp(-x)). - _G. C. Greubel_, Jan 05 2018

%t Table[n*(6*n^2+22*n+3*((-1)^n+7)), {n,1,40}] (* _G. C. Greubel_, Jan 05 2019 *)

%o (PARI) vector(40, n, n*(6*n^2+22*n+3*((-1)^n+7))) \\ _G. C. Greubel_, Jan 05 2019

%o (Magma) [n*(6*n^2+22*n+3*((-1)^n+7)): n in [1..40]]; // _G. C. Greubel_, Jan 05 2019

%o (Sage) [n*(6*n^2+22*n+3*((-1)^n+7)) for n in (1..40)] # _G. C. Greubel_, Jan 05 2019

%o (GAP) List([1..40], n -> n*(6*n^2+22*n+3*((-1)^n+7))); # _G. C. Greubel_, Jan 05 2019

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Jul 11 2011